Turbo-machine blade spacing with modulated pitch



Oct. 31, 1961 3,006,603

W. J. CARUSO ETAL TURBO-MACHINE BLADE SPACING WITH MODULATED PITCH Filed Aug. 25, 1954 4 Sheets-Sheet 1 William J.Ca 0

Boris M. Wu

Their- Attorngg 31, 1961 w. J. CARUSO ETAL 3,006,603

TURBO-MACHINE BLADE SPACING WITH MODULATED PITCH Filed Aug. 25, 1954 4 Sheets-Sheet 2 FREQU l 1 n n 8 DISTANCE AROUND CIRCUMFERENCE 2 70" Inventor-s: William J. Caruso Boris M. Wundt P", CIRCUMFERENTIAL Pn-cH OF STRUCTURE Oct. 31, 1961 w. J. CARUSO ETAL 3,005,603

TURBO-MACHINE BLADE SPACING WITH MODULATED PITCH Filed Aug. 25, 1954 4 Sheets-Sheet 3 E F F l I I I l l x l TI 0 F 'i-AF I l 3 l I o 90' I80 270 360' DlSTANCE AROUND CIRCUMFERENCE Fig.6. I K-VBRATION STIMULUS WlTHOUT MOOULATED ARRANGEMENT I004 m 90 D 5' 80 E m 70 Z 9 60 fg so 9 40 DJ 2 3o 3 u: 20 I 0 l l l I f B, MODULATION INDEX (AF, MAXIMUM FREQUENCY DEVIATION WHEN MODULATION FREQUENCY f=|) Invent or-s: William J.Car-uso Box-ls M. Wundt Their Attorneg Oct. 31, 1961 w. J. CARUSO ETAL 3,006,503

RBO- CHINE BLADE NG WITH MOD led Aug. 25, 1954 4 Sheets-Sheet 4 a DDDDDDDDDDDDDD ER Z E 'Z THHHHHHmIHTUHHUTTT 46 48 5O 52 S4 55 58 6O 52 54 66 68 7O 72 74 47 49 SI 53 55 57 59 i 6! 63 65 67 69 7| 73 75 Inventors: Wilham J. Caruso Boris M.Wundt EiL Their" Attorneg United States Patent 3,006,603 TURBO-MACHINE BLADE SPACING WITH MODULATED PITCH William J. Caruso and Boris M. Wundt, Fitchburg, Mass, assignors to General Electric Company, a corporation of New York Filed Aug. 25, 1954, Ser. No. 452,036 13 Claims. (Cl. 253--39) This invention relates to a novel theory and method for reducing the maximum value of the stimulus applied to mechanical systems subject to vibration, particularly as applied to the problem of reducing destructive vibrations in rotating machinery such as fluid-dynamic apparatus like axial or radial flow turbo-machines having a circumferential row of nozzles delivering motive fluid to a relatively rotating bucket-Wheel.

In such a machine, each nozzle imparts a discrete impulse to each bucket passing by the nozzle. If the nozzles are of equal circumferential pitch and equally spaced, as is usually the case in prior art turbo-machines, a given bucket will receive such impulses at a frequency depending on the speed of rotation of the bucket-wheel relative to the stationary nozzles, and on the number of nozzles comprising the complete nozzle circle. It is always necessary to correlate the many factors involved (which are further complicated by the fact that the turbine wheel will have to operate over a range of speeds) so that the exciting impulses imparted to the buckets will not result in destructive vibration amplitudes within the normal operating range of the machine. This is difficult and sometimes even impossible to achieve with the prior art turbo-machine designs. Once the turbine designer ascertains the range of exciting frequencies which will be imparted to a given bucket over the intended operating range of the machine, it is his problem to so design the blade structures that they will have no natural frequency of vibration coinciding with any of the exciting frequencies likely to be impressed on the bucket.

In the past, the enormous complexity of this problem has resulted in numerous rule-of-thum design methods based on long years of practical experience, by which turbine designers have determined the material and shape, and the number and disposition of rotating and stationary blades, in order that buckets designed and manufactured by available techniques can withstand the vibration stimuli encountered.

A study of the basic theory of vibration phenomena associated with turbo-machine nozzles has led us to the discovery that there are certain striking similarities in the mathematical analysis of such phenomena and the analysis of cyclical electrical phenomena, namely certain mathematical theories used in radio-communication. Analytical studies along such lines have led to the discovery that the principles of so-called frequency modulation broadcasting can be adapted to the design of the arrangement of buckets in the rotating turbine bucketwheel and to the arrangement of nozzles in the stationary nozzle ring, and to various other analogous structures, in such a manner as to achieve a very great reduction in the stimulus which is applied to that member subject to destructive vibration, such as the stationary nozzle blades, and/ or the buckets on the rotating wheel, etc.

Accordingly, an object of the present invention is to provide an improved arrangement of adjacent moving and stationary members disposed in a fluid stream, whereby the stimulus imparted to the vibrating members is minimized.

A further object is to provide an improved arrangement for reducing vibration stresses in the associated nozzles and blades of a turbo-machine such as an axial 3,006,603 Patented Oct. 31, 1961 or radial flow turbine, or an axial or radial flow compressor, or an analogous machine.

A still further object is to provide an improved design method for the arrangement of turbo-machine nozzles and blades (or buckets) which lends itself readily to mathematical analysis by methods developed in the elec trical communication arts, without resort to the empirical or rule-of-thumb design methods which previously had to he reliedupon.

Another object is to provide a turbo-machine design method which effects substantial reductions in the noise level of the machine.

Other objects and advantages will become apparent, and the improved design method will be understood from a consideration of the following description taken in connection with the accompanying drawings, in which FIG. 1 is a diagrammatic plan view of a turbine nozzle ring having a complete circumferential row of nozzles designed in accordance with the invention; FIG. 1a is a diagrammatic representation of a bucket-wheel intended to be used with the nozzle ring of FIGURE 1; FIGS. 2, 2a show a conventional nozzle ring and a bucket wheel designed in accordance with the invention; FIGS. 3, 3a represent a nozzle ring and bucket wheel both incorporating the characteristic feature of this invention; FIGS. 4, 5, 6 and 7 are graphical representations of certain design characteristics and results achieved with a turbo-machine nozzle ring or bucket wheel designed in accordance with FIGS. 1, 2, and 3; and FIGS. 8, 9 and 10 illustrate the application of the invention to centrifugal compressors.

Generally stated, the invention is practiced by designing one or both of the cooperating members of a turbomachine stage so that the frequency at which successive impulses are imparted by fluid-dynamic forces to the associated member changes continuously and progressively, throughout one complete revolution of the rotating member. A single pattern of frequency changes occurring only once in each revolution, results in optimum reduction of stimulus.

In describing this novel design method, the following definitions and notations will be employed, in explaining one example of a particular application.

D=2R pitch diameter, the mean or nominal diameter of the fluid-delivering nozzle member (see FIG. 1).

P circumferential distance between similar points on adjacent fiuiddelivering nozzles, the required variation of which is determined in accordance with the modulated pitc method described below.

F frequency, the integral number of fluid-delivering nozzles which would be included in a complete circumferential row of the modulated pitch member if all the nozzles had the same circumferential pitch P as that of a given nozzle. As evidenced by the formula F varies inversely with P.

F median frequency, a particular frequency F representing an average frequency which occurs at some point around the circumference from the starting point 0, as defined below.

Af frequency deviation at a given location along the circumference fiom median frequency F (see FIG. 4).

AF maximum frequency deviation from the median frequency F other words, maximum value of M (see FIG. 4).

0 starting point, the location in the circumferential row of modulated pitch nozzles at which the single 3 pattern of frequency changes begins and ends (see FIG. 1).

The significance and interrelation of these factors will become apparent from the following description of the theory and practice of this modulated pitc turbomachine design.

FIG. 1 is a purely diagrammatic representation of the nozzle ring of an axial flow turbine in which the nozzle blades, one edge of each of which is identified by the radial lines 1, are spaced circumferentially in accordance with our modulated pitch theory. It will, of course, be appreciated by those familiar with turbine design that this nozzle ring comprises annular concentric wall members 2, 3 which with each pair of adjacent radial partitions 1 defines a fluid delivering nozzle. The complete ring of nozzles does not form a homogeneous annular stream of fluid, but instead produces a series of disturbances in the fluid stream, by reason of the finite thickness of'the nozzle partitions 1.

The pitch diameter D of the nozzle ring and the circumferential pitch P of a single nozzle are identified on FIG. 1. The starting position is at 12 oclock.

In accordance with one embodiment of the invention, each nozzle (except at O) has a pitch P which is slightly larger than the preceding nozzle, and slightly smaller than the succeeding nozzle. That is, the first nozzle 1a has the smallest circumferential pitch P of any nozzle in the ring, and the last nozzle lz has a larger circumferenti-al pitch P than any other. The intermediate nozzles increase in pitch progressively in the clockwise direction by a specified increment. The manner in which this increase in pitch of the nozzles is determined will be seen in more detail from the following discussion of FIGS. 4, 5, 6 and 7.

It is to be assumed that a special nozzle ring in accordance with FIG. I will have an associated bucket-wheel, as illustrated in FIG. la, with a shaft 7a, disk 7b, and a plurality of radially disposed vanes (or buckets) 70, which will ordinarily be equally spaced around the circumference of the wheel. If the nozzle ring consists of 24 nozzles, as in FIG. 1, then a given bucket 7c rotating 360 clockwise from the 0 position will be acted upon by 24 discrete impulses from the nozzles 1a, 1b, 1c, 1d 12. If these 24 nozzles were of identical pitch and uniform distribution around the nozzle ring, then a given bucket would experience 24 evenly spaced impulses during each revolutionof the bucket-wheel. Because the nozzles, in accordance with the invention, are not of equal circumferential pitch, it is necessary to introduce and define the concept of the frequency, identified F in the above notation, which corresponds to .the pitch P of a given nozzle. 7

Accordingly, the frequency of a given nozzle is defined as the integral number of nozzles which would constitute a complete360 ring if all were equal in pitch to the nozzle in question and uniformly distributed throughout the circle. Thus, for example, the minimum pitch nozzle 1a may have a frequency F of 34, since it would require this many nozzles identical to 1a to make a complete 360 ring of nozzles of pitch diameter D. Similarly, the frequency of the last nozzle 11 may be 14, since that many identical nozzles would be required to 7 make a complete ring of the same pitch diameter D.

Thus, for the purpose of this discussion, the irequency of a given fluid-delivering nozzle member is defined as the number of identically spaced nozzles required to form a complete ring. And, to each nozzle in the ring can be assigned a frequency F, which decreases continuously in the clockwise direction, as the circumferential pitch P a of the nozzles increase.

quency modulation method of varying the frequency of 4 the impulses applied by the fluid disturbances to the moving buckets.

The precise manner in which the frequency of the nozzle varies around the circumference of the nozzle ring, and the manner in which the change in circumferential pitch P of the nozzles is determined, will now be described.

In FIG. 4 the median frequency F is represented by the broken horizontal line. The initial frequency, that of nozzle 1a, is indicated by the maximum ordinate of the curve 4. The minimum ordinate of the curve, at the 360 point, represents the frequency of the last nozzle lz. It is to be observed that the deviation of the frequency of a given nozzle from the median frequency F is denoted by the symbol Af. The maximum deviation of the frequency of any nozzle from the median frequency F is denoted by AF. It is to be particularly noted that the maximum positive deviation AF of the bucket 1a from the median F is equal in magnitude to the maximum negative deviation of the frequency of bucket lz. In this example, curve 4 is actually drawn as a straight line. In other words, the frequency is modulated as a straight-line function of distance from 0 around the circumference of the nozzle ring. To be completely rigorous, the curve 4 would have to be represented by a series of discontinuous points, each point being on the curve at a location along the abscissa corresponding to the middle of the nozzle which the point represents, since there is only one frequency for each nozzle and each nozzle has a finite pitch P. However, for design purposes, the curve 4 is drawn as a continuous line and then used to ascertain the precise pitch required for each nozzle as follows.

In using this design method, it will be first necessary to ascertain the nominal pitch diameter D of the nozzle ring and the approximate number of nozzles desired in 360. This will be done in accordance with the turbine designers experience concerning the optimum height-towidth or aspect ratio for a turbine nozzle, and other well-known factors. It is also necessary to select the median frequency, which will ordinarily be the number of nozzles in a complete ring of the same nominal diameter D that would be used in accordance with previously known turbine design methods. In addition, the integral number representing the maximum deviation AF from this median frequency must be selected. For instance, in the example represented by FIGS. 1 and 4, assume that the selected median frequency F is 24 and that the selected maximum deviation in frequency AF is 10. It follows that the frequency of nozzle 1a will be 34 and the frequency of nozzle 12 will be 14. This means that the circumferential pitch P of the nozzle 1a will occupy of the circumference of the nozzle ring. The frequency of nozzle 1a is represented in FIG. 4 on curve 4 by the ordinate (F -|AF) at the 0 point on the abscissa.

FIG. 5 is a plot of the resulting circumferential pitch P of succeeding nozzles, and is derived from FIG. 4 by the formula Here again, the abscissa represents the distance around the pitch circle of the nozzle ring from the starting point 0; and the ordinate represents the circumferential pitch P. It will be apparent that the nozzle pitch curve 5 is an inverse function of the frequency curve 4 in FIG. 4. Specifically, the nozzle pitch P is represented by the general expression mzhAf The pitch P corresponding to the frequency of nozzle 1a is represented in FIG. 5 on curve 5 by the ordinate at the point on the abscissa. The specified pitch 1a is now laid oif along the abscissa of FIG. starting at 0, and the ordinate of curve 5 at this point on the abscissa defines the second nozzle pitch 1b. Accordingly, the pitch 1b is laid ofi next to la; and then the ordinate of curve 5 at this point on the abscissa defines the third nozzle pitch 1c. Repetition of this process will determine the circumferential pitches of succeeding nozzles around the periphery of the nozzle ring.

It will, of course, be understood by turbine designers that it is necessary to take into consideration the finite thickness of the nozzle partitions in determining the pitch of the nozzles. It is also necessary to limit the maximum variation in nozzle pitch, defined by the maximum frequency deviation AP, to a value which will be acceptable from the standpoint of aerodynamic performance. It may even be necessary to make the shape of the nozzle passages of different aerodynamic designs, in accordance with the van'ation in pitch, in order to achieve as large a maximum frequency deviation as possible, while retaining good aerodynamic performance from all nozzles.

Analysis of a nozzle ring pitch modulated as in FIG. 1 by the mathematical theories applicable to radio frequency modulation, shows that the above discussed arrangement reduces the stimulus to a practical minimum for a specified frequency deviation AF. Although the complexities of such mathematical theory make it impractical to go into details here, some fundamental definitions and relationships will be discussed briefly in order to better understand the advantages, theory, and design philosophy behind this invention.

If the nozzles were distributed around the circumference of the nozzle ring (of pitch radius R) with a uniform pitch P, to which corresponds a constant frequency F, then the distribution of the magnitude of discrete impulses caused by the nozzle partitions may be described conventionally as Ya Y sin Y sin (a) where Y is a constant amplitude of the sinusoidal disturbance, x is the variable central angle in radians, and S=P/R is the central angle which corresponds to pitch P at radius R. Phase and is a constant along the circumference and equal to F.

However, if

is not constant but varies along the circumference, as in a pitch-modulated nozzle ring, then becomes which is an instantaneous value of the pitch angle and instantaneous phase and Equation a becomes more general, thus Ye Y sin U (c) It is convenient to replace angular pitches S by the corresp onding frequencies 21r EE Equation c becomes then, in terms of frequencies,

Y(x)=Y sin [fF dx] ((1) Consider a nozzle ring, as above, with nozzles of equal pitch and frequency F the median frequency, which Will be designated from now on as carrier frequency F This carrier frequency F, is varied or modulated along the pitch circle of the nozzle ring. Theoretically, the cycle of modulation may repeat itself an integral number of times around the nozzle ring, in which case the number of such repetitions is called the modulation frequency f. The carrier frequency F may be modulated in any desired manner. For the purpose of clarity we assume that the variation of frequency F within a modulation cycle takes place in a sinusoidal manner, as in present day FM radio transmission. The amplitude of modulating sinusoid we designate as AF and define as maximum frequency deviation.

The modulating frequency is then AF sin fx and the modulated carrier frequency F becomes F =F +AF sin fx (e) Amplitude (Equation 0) will become Y(x) Y sin [I(F,+AF Sin fx)dx] or after integration Y(:v) Y sin |:F,,X f cos fan] Y(x) :1 sin [F X/3 cos fx] and phase becomes =fF dx=F X-fi cos fx (g) Where:

X is the variable central angle F is carrier frequency f is modulation frequency AF is maximum frequency deviation AF g 7 {i=7 15 the Modulation Index Y is the amplitude of the sinusoidal disturbance Y is the local magnitude of disturbance corresponding to angle X.

The physical meaning of Equation e becomes clear after it is expanded into a Fourier Series:

Fourier expansion indicates that a sinusoidal modulation with frequency deviation AF, modulation frequency f and modulation index [3 of a carrier frequency P with amplitude Y results in the following:

(a) In addition to the carrier frequency F an infinite number of harmonic oscillations with other frequencies occurs. These frequencies are F -|-f, F f, F +2f, F 2f, F +3f, F -3f, F +nf, F -nf, etc. They are spaced apart by the modulation frequency f. The higher frequency components above the carrier frequency are called upper sideband frequencies and the lower frequencies below the carrier frequency lower sideband frequencies. However, for practical purposes all components with significant amplitudes are confined within a frequency band equal to twice the maximum frequency deviation 2AF. In other words the frequency modulation 7 creates a whole-band of other frequencies on both sides of the carrier frequency F (b) The new amplitude of the'carrier frequency F and the amplitudes of the new sideband frequencies are 7 equal to the unmodulated amplitude of the carrier fiequency Y multiplied by certain coefficients, all less than 1. The coefficients are values of Bessel functions (first kind) whose order is equal to the order of the particular sideband frequency and whose argument is modulation index ,8. The coefficient for the new amplitude of the carrier frequency F is equal to the value of Bessel function of zeroth order for the same index 5.

(c) The energy content of each harmonic is proportional to the square of its amplitude, therefore, the whole the amplitudes of harmonics differ considerably and some are not a small fraction of the unmodulated carrier amplitude. Only when 6 reaches very large values (appreaching infinity) is this theoretically possible for sinusoidal modulation.

(d) It has been discovered that, if the number of modulation cycles 1 was limited to only one in a complete nozzle ring (i.e. f=l) and if the manner of modulation was confined to a gradual and preferably uniform or -almost uniform increase of frequency, from a minimum a value to a maximum value once in 360, then the energy was effectively and almost uniformly dispersed throughout the band width, also for practically acceptable values of 5.

(e) The previously discussed linear or saw-tooth modulation of carrier frequency F shown in FIGURE 4, very efficiently disperses energy throughout band width ZAF.

FIGURE 7 shows the amplitude frequency spectrum for a nozzle ring with F =60, maximum frequency deviation AF: 14, modulation frequency i=1; and

It can be seen that the maximum amplitude of any harmonic in the spectrum does not exceed 22% of the unmodulated amplitude of the carrier. The reduction of stimulus achieved by modulating with such a single sawtooth (linear) cycle is shown in FIGURE 6. Here the abscissa of curve 6 is the modulation index 5, which for this case, when f l, is identical with maximum frequency deviation AF. The ordinate of curve 6 represents the maximum sideband amplitude as a percentage of the amplitude of the unmodulated carrier. t is seen that for a maximum frequency deviation of 4, the maximum amplitude is 42% of the unmodulated carrier; and a AP of 16 reduces the amplitude to only 21% of its original magnitude.

the stimulus obtained with a conventional unmodul-ated nozzle ring.

While so far the invention has been described as 'applied to the stationary nozzle ring of an axial flow turbine, it may also be applicable to the rotating wheel. In

this case the stationary nozzles might be of uniform pitch and'distribution around'the nozzle ring; andthe modulation theory would be applied to the arrangement of the buckets on the moving Wheel. Such an arrangement is illustrated in FIGS. 2 and 2a, in which the stationary nozzle ring has identical nozzles 7 designed in accordance with conventional turbine practice, while the rotating bucket wheel 8 has a plurality of buckets 9 spaced in accordance with the modulated pitch theory. That is, the initial'bucket 9a is of a minimum pitch and maximum frequency,.while the last bucket 9z has a maximum pitch and minimum frequency. I

' Furthermore, the modulated pitch design may be applied to both the stationary nozzle ring and the moving bucket wheel, as illustrated in FIGS. 3, 3a. Here, the stationary nozzles 10 are spaced similarly to the nozzles 1 of FIG. 1, while the moving buckets 11 are spaced as described in connection with the buckets 9 of FIG. 2a.

The invention may also be applicable to analogous turbo-machinery, for instance centrifugal compressors having a rotor with radial vanes defining rotating fluiddelivering nozzles, the disturbances created by which affect the stationary blades or vanes in the diffuser of the compressor. FIG. 8 illustrates such an application, in which the centrifugal impeller 12 has radial blades 12a 12z ofmodulated pitch, while the diffuser vanes 13' define identical diffusing passages 13a evenly spaced around the circumference of the impeller.

FIG. 9 illustrates how the modulation theory may be applied to stationary dilfuser vanes 14 associated with equi-spaced and identical impeller blades 15.

Or, the modulated spacing may be applied to both the stationary and moving members of a centrifugal machine, as illustrated in FIG. 10. Here the rotating wheel has blades 16 with a modulated spacing, as shownin connection with the blades 12 of FIG. 8; and the stationary member has blades 17 modulated as shown in connection with the diifuser vanes 14 of FIG. 9.

' delivered inwardly therefrom drive the central rotor.

Likewise, the axial flow structures of FIGS. 1, 1a, 2, 2a, 3, 3a may be considered to be stages of axial flow compressors. With respect to FIGS; 1, 1a, it is comparatively easy to see how, as described above in connection with the design method and data presented in FIGS. 4, 5, 6, 7, the invention works when the modulated stationary nozzles of'F IG. 1 are delivering jets of varying frequency to the rotating buckets 7c of FIG. 1a. It is apparent that a given bucket 70 will experience impulses of progressively changing frequency as it rotates 360 from the initial position 0 past the variably spaced nozzles of FIG. 1. However, it is not quite so obvious why the modulated spacing of the buckets in FIG. 2a has a beneficial efiect on the vibration characteristics'of the structures.

In this connection, it is to be noted that the radially extending nozzle partitions which form the uniformly pitched nozzles 7 of FIG. 2 are also subject to destructive vibration forces. Even though the fluidis flowing from nozzles 7 to the bucket wheel 8, a given nozzle blade will experience an impulse each time a bucket 9 passes. This is because passage of the closely adjacent bucket 9 produces a small local disturbance in the fluid pressure distribution adjacent the exit edges of the stationary nozzle blades, and the passage of this small pressure disturbance results in the application of a vibrationinducing impulse to the radially extending wall partition of the stationary nozzle member. Thus, modulating the pitch ofthe moving buckets 9 as in FIG. 24; has a beneficial effect in reducing the vibration forces applied to the radially extending nozzle partitions or blades of the stationary nozzle ring member 7.

Likewise, with respect to the centrifugal compressor of FIG. 8, the fluid is flowing from the radially extending impeller passages defined between the modulated blades 12 into the stationary passages defined between the diffuser vanes 13. The rotor 12 is in effect a rotating nozzle member delivering discrete fluid jets into the passages 13a defined between the stationary vanes 13. The vibration characteristics would be substantially the same if rotor 12 were held stationary and the annular diffuser member carrying the vanes 13 were permitted to rotate as a radial flow turbine bucket-wheel. In either case, the modulation of the spacing of the fluid-delivering members 12a prevents destructive vibration forces being built up in the cooperating annular row of blades 13. Furthermore, if the structure of FIG. 9 is considered a radial in-flow turbine, then it will be obvious that the motive fluid delivered inwardly through the passages a 152 so as to drive the rotor 15 would have quite similar vibration characteristics to the modulated pitch nozzle of FIG. 1 cooperating with the uniformly spaced buckets of FIG. la. But it will also be appreciated by those familiar with the centrifugal compressor art that each of the uniformly spaced rotor blades 15 of FIG. 9 experience a slight impulse due to changes in local pressure distribution around the adjacent edges of the respective diffuser vanes 14, caused by passage of the rotor blades, so that the modulated pitch of vanes 14 prevents destructive vibrations being set up in the tip portions of the compressor blades 15.

It may also be noted that it is not necessary that the number of the fluid-passing nozzles be equal to the number of the associated relatively rotating structures. Thus in FIG. 1 the stationary nozzle comprises 24 modu lated pitch nozzles, while the bucket wheel of FIG. 1a has 32 blades or buckets 70. In FIG. 2 the stationary nozzles are shown with uniformly pitched members, while the bucket wheel in FIG. 2a has 24 modulated pitch blades. By the same token, the modulated pitch nozzle ring of FIG. 3 need not have the same number of elements as the modulated pitch bucket wheel of FIG. 3a.

Nor is it necessary that the change in frequency should occur in the same direction on each member. In FIG. 3 and 3a the pitch of the nozzles 10 and the pitch of the buckets 11 both increase in the clockwise direction. This is not necessary, and in FIG. 10 the rotor blades are spaced with an increasing pitch in the clockwise direction, while the stationary diffuser blades have an increasing pitch in the counterclockwise direction.

The above discussion of the various possible permutations and combinations will show that the important criterion in the practice of the invention is that, if a given one of a pair of adjacent relatively rotatable members has a portion subject to destructive vibration forces, then any adjacent discontinuities in the other member may advantageously be spaced in accordance with the modulated pitch theory of the invention in order to prevent such destructive vibration. It is immaterial which member is stationary and which is moving, and it is likewise immaterial whether the fluid is flowing from the modulated pitch member towards the member subject to vibration, or in the reverse direction, or if the adjacent relatively rotatable members are not actually delivering a continuous flow of fluid from one to the other but are merely rotating adjacent each other so that a pressure distribution is created by circumferentially spaced discontinuities on the rotating bodies, so that the small local pressure irregularities tend to set up vibrations in the vibration-responsive portions of the other member.

The invention is also applicable to other rotating structurm, such as fans, propellers, etc. The intensity of the aerodynamic noise level of such apparatus may be greatly reduced by appropriately modulating the spacing of the fluid-delivering or fluid-passing nozzle members. In such apparatus, the advantages of noise level reduction will be obtained even though there is no stationary member associated with the rotor subject to mechanical vibrations. In other words, the noise is caused by vibration or discontinuity of the fluid stream itself. Thus it will be apparent that an axial flow fan or propeller having no associated stationary diffuser member exerts somewhat of a siren effect on the column of air moving through it. That is, the rotating impeller serves to interrupt the uniform column of fluid moving through the rotor and these periodic interruptions generate a frequency which shows up as noise. If the interruptions are uniform, then a definite pitch of sound will be produced. By appropriately modulating the fluid-passing members, the net average noise level can be greatly reduced.

Thus it will be seen that the invention provides a basically new approach to the theoretical design of rotating fluid-dynamic machinery in which a fluid-passing member produces a cycle of disturbances in the fluid flow which are likely to set up sound waves and destructive vibrations in associated members. By use of the principles of frequency modulation radio transmission, as outlined herein, it appears possible to reduce the vibration stimulus applied to the associated vibrating member to a degree wholly impossible with the design methods known to the prior art.

While only a few applications of the theory have been described specifically herein, it will be obvious to those skilled in the art that many other applications may be made; and it is of course intended to cover by the appended claims all such modifications as fall within the true spirit and scope of the invention.

What we claim as new and desire to secure by Letters Patent in the United States is:

1. In a fluid-dynamic machine, the combination of first and second relatively rotatable members, one of which defines an annular row of fluid-passing nozzle members, the other of which has a circumferential row of members subject to vibration, said nozzles having a frequency of spacing which changes substantially uniformly and progressively in the same direction, the pattern of frequency changes occurring only once throughout each 360 of relative rotation.

2. In a fluid-dynamic machine, the combination of first and second relatively rotatable members one of which defines an annular series of fluid-delivering nozzle members and the other of which has at least one member receiving impulses from the jets delivered by said nozzles and having a tendency to vibrate at an inherent natural frequency, means causing the frequency of the vibration impulses applied to the fluid-receiving member to vary in discrete increments progressively and substantially uniformly throughout each 360 of relative rotation of the fluid-delivering and fluid-receiving members, the single pattern of such frequency changes occupying the full 360 of such relative rotation, whereby the net effective vibration stimulus applied to the fluid-receiving member is reduced.

3. In a fluid-dynamic machine, the combination of a first stationary member and a second associated relatively rotatable member, the stationary member comprising an annular series of fluid-passing nozzles and the rotating member having a plurality of uniformly spaced structures subject to vibration induced by the fluid discharged from the stationary member, said nozzles having a fresquency of spacing which increases progressively and substantially uniformly from a minimum frequency to a maximum frequency, the pattern of said frequency changes occurring only once around the complete periphery of the stationary nozzle member.

4. In a fluid-dynamic machine, the combination of a first stationary member and a second relatively rotatable member, the rotating member having a circumferential row of discrete structures, the stationary member having an annular row of uniformly spaced fluid-passing nozzles with wall portions subject to vibration from impulses caused by the passage of the structures on the associated rotating member, said rotating structures having a frequency of spacing which changes progressively and sub- 11 stantially'uniformly from a minimum frequency to a maximum frequency, the pattern of said frequency changes occurring only once around the complete periphery of the rotating member.

5. In a fluid-dynamic machine, the combination of first and second relatively rotatable members one of which defines an annular row of fluid-passing nozzle members and the other of which has at least one member receiving fluid impulses derived from said relative rotation, the frequency of the spacing of said nozzle members vary ing progressively and substantially uniformly, the single pattern of said frequency changes occupying the full 360 of the nozzle member, whereby the net effective vibration stimulus imposed on said other member is reduced.

6. In a fluid-dynamicmachine, the combination of a first member defining an annular row of fluid-passing structures, and at least one relatively rotatable second member adjacent said first member and subject to vibration, said fluid-passing structures having a fraquency of spacing which changes progressively, in discrete increments and substantially uniformly from a minimum frequency to a maximum frequency, the pattern of said frequency changes occurring only once around the complete periphery of the first member.

7. In a fluid-dynamic machine, the combination of a first member and a second adjacent and relatively rotatable member, said first member having'an annular series of fluid-passing nozzles including wall members subject to vibration due to fluid impulses derived from the passage of discrete portions of the adjacent second member, said second member having an annular row of fluid-passing structures with portions also subject to vibration clue to fluid impulses derived from relative motion of the nozzles of said first member, said relatively rotatable structures each having a frequency of spacing which changes progressively and substantially uniformly, the respective patterns of said frequency changes occurring only once around the periphery of the respective members.

8. In an axial flow turbine, the combination of a stationary member defining an annular row of fluid-delivering nozzle members, a bucket wheel'supported for rotation concentric with said nozzle ring and having a circumferential row of equally spaced bucket members having a tendency to vibrate due to the impulses from the fluid jets from said nozzles, the nozzles being of a circumferential width which changes progressively and substantially uniformly throughout the full 360 of the nozzle ring, whereby the frequency of spacingof the nozzles is modulated according to a single pattern of changes progressively and substantially uniformly in the same direction throughout each complete revolution of the bucket Wheel relative to the nozzle ring.

9. In a fluid-dynamic turbo-machine, the combination of a stationary member defining an annular row of fluid-delivering nozzles, a relatively rotatable wheel adjacent said stationary member and having an annular row of equally spaced bucket members adapted to receive motive fluid from said nozzles, the nozzles of said stationary member having a frequency of spacing which changes substantially uniformly and progressively in the same direction, the pattern of frequency changes occurring only once around the periphery of the nozzle ring 12 member, whereby the vibration stimulus applied to the moving buckets by 'the' jets issuing'from said nozzles is reduced. V

10. In afluid-dynamic turbo-machine, the combinationof a first nozzle ring member having an annular row of uniformly spaced nozzles having wall portions subject to vibration, a relatively rotatable bucket wheel having a'circumferential row of bucket members adapted to receive motive fluid from said stationary nozzle ring, the frequency of spacing of said buckets changing progressively in the same direction and substantially uniformly, the pattern of frequency changes occurring only once around the complete periphery of the bucket wheel.

11. In a fluid-dynamic turbo-machine, the combination of'a first nozzle member-with an annular row of fluid delivering nozzles, a relatively rotatable wheel having 'a circumferential row of blades adapted to receive motive fluid from said nozzles, both said nozzles and said blades having a frequency of spacing which changes progressively and substantially uniformly, the pattern of said frequency changes occurring only once around the complete periphery of the respective nozzle and wheel members.

12, In a radial flow turbo-machine, the combination of an inner memberhaving an annular row of radially extending vane members defining fluid passages, and an outer annular memberconcentric with said inner member and having an annular row of spaced vane members defining radially' extending fluid passages, at least one of said annular rows of vanes being unequally spaced to provide a frequency of spacing which changes progressively and substantially uniformly, the pattern of said frequency changes occurring only once around the complete periphery of the member, whereby vibration resulting from'the fluid impulses derived from the relative rotation of the variably spaced anular row of vanes and imposed on the vanes of the other. annular row are reduced. 1

13. A fluid-dynamic machine having a. rotating member with a circumferential row of fluid-passing structures, the frequency of spacing of said structures changing progressively and substantially uniformly around the periphery of the member, the single pattern ofv said. frequency changes occupying the entire 360 of the periphery of the member, wherebythe net average noise level of the discrete fluid jets passing said structures is reduced.

References Cited in the'file of this patent UNITED STATES PATENTS Campbell July 29, 1924 Campbell ..7 July 29, 1924 1,525,814 Lasche Feb. 10, 1925 1,534,721 Lasche Apr. 21, 1925 60 Tangential Vibration of Steam Turbine Buckets, by Campbell and Heckman, ASME Transactions, vol. 47, 1925, pages 643-671. V a 

